On interior and boundary regularity of weak solutions to a certain quasilinear elliptic system.
On interior regularity criteria for weak solutions of the navier-stokes equations.
On internal approximations of parabolic problems
On invariant measures for some infinite-dimensional dynamical systems
On invariants of continuous subgroups of the generalized Poincaré group .
On irrotational flows through cascades of profiles in a layer of variable thickness
The paper is devoted to the study of solvability of boundary value problems for the stream function, describing non-viscous, irrotional, subsonic flowes through cascades of profiles in a layer of variable thickness. From the definition of a classical solution the variational formulation is derive and the concept of a weak solution is introduced. The proof of the existence and uniqueness of the weak solution is based on the monotone operator theory.
On Isometric Immersions of the Hyperbolic Plane Into the Lorentz-Minkowski Space and the Monge-Ampère Equation of a Certain Type.
On iterations of Green type integrals for matrix factorizations of the Laplace operator
Convergence of special Green integrals for matrix factorization of the Laplace operator in is proved. Explicit formulae for solutions of -equation in strictly pseudo-convex domains in are obtained.
On iterative solution of nonlinear heat-conduction and diffusion problems
The present paper deals with the numerical solution of the nonlinear heat equation. An iterative method is suggested in which the iterations are obtained by solving linear heat equation. The convergence of the method is proved under very natural conditions on given input data of the original problem. Further, questions of convergence of the Galerkin method applied to the original equation as well as to the linear equations in the above mentioned iterative method are studied.
On Jeffreys model of heat conduction
The Jeffreys model of heat conduction is a system of two partial differential equations of mixed hyperbolic and parabolic character. The analysis of an initial-boundary value problem for this system is given. Existence and uniqueness of a weak solution of the problem under very weak regularity assumptions on the data is proved. A finite difference approximation of this problem is discussed as well. Stability and convergence of the discrete problem are proved.
On Kakeya–Nikodym averages, -norms and lower bounds for nodal sets of eigenfunctions in higher dimensions
We extend a result of the second author [27, Theorem 1.1] to dimensions which relates the size of -norms of eigenfunctions for to the amount of -mass in shrinking tubes about unit-length geodesics. The proof uses bilinear oscillatory integral estimates of Lee [22] and a variable coefficient variant of an " removal lemma" of Tao and Vargas [35]. We also use Hörmander’s [20] oscillatory integral theorem and the Cartan–Hadamard theorem to show that, under the assumption of nonpositive curvature,...
On Kato's inequality for the Weyl quantized relativistic Hamiltonian.
On Kelvin type transformation for Weinstein operator
The note develops results from [5] where an invariance under the Möbius transform mapping the upper halfplane onto itself of the Weinstein operator on is proved. In this note there is shown that in the cases , no other transforms of this kind exist and for case , all such transforms are described.
On Kirchhoff type problems involving critical and singular nonlinearities
In this paper, we are interested in multiple positive solutions for the Kirchhoff type problem ⎧ in Ω ⎨ ⎩ u = 0 on ∂Ω, where Ω ⊂ ℝ³ is a smooth bounded domain, 0∈Ω, 1 < q < 2, λ is a positive parameter and β satisfies some inequalities. We obtain the existence of a positive ground state solution and multiple positive solutions via the Nehari manifold method.
On Korn's second inequality
On KP-II type equations on cylinders
On -convergence of Rothe’s method
On -regularity for the gradient of a weak solution to nonlinear elliptic systems
Interior -regularity for the gradient of a weak solution to nonlinear second order elliptic systems is investigated.
On -estimates for hyperbolic systems
On -estimates for solutions of elliptic boundary value problems